As others have pointed out before me, this movie is most definitely a drama but does have comedic segments in order to appeal to its younger viewers. These comedy scenes are not the main focus of the movie, however. The film deals with darker themes (betrayal, guilt, facing the past in order to find yourself and move forward) that don't normally tend to appear in comedy movies and that's why I feel it's mostly a drama.
Like most Disney classics, it takes an original story and turns it into a charming animated movie that can be enjoyed by anyone. I mean Disney films have always been more musicals than any other genre to me but musicals in their self can be their own sub genre of comedy or drama. Out of the two I'd say it was drama but I'd sooner put it into an animated adventure category of some sort.
Then again I never really think about genres... I just like things, I don't typically care about the genre, because ultimately the only thing that matters to me is the overall quality and whether I like it or not.
I have to agree with most of the posters above (re: drama with comic elements)
Like a lot of good kids media (books, tv, films etc) it takes some dark, and important themes and makes them understandable. It also gives kids a framework for them to talk about their own feelings.